We use here the notation from [1]}: at each stage \(i \in \lbrace 1..m\rbrace \) , the algorithm is producing lists of \(S_i\)  vectors with weight \(p_i\)  on an information set and weight \(\left(\omega _h^{(i)} \right)_{h \in \lbrace 1..i\rbrace }\)  on redundancy subsets of respective length \(\left(\ell _i \right)_{h \in \lbrace 1..i\rbrace }\) . Since the list at the final stage \(m\)  contains the solution, the decoding distance \(\omega \)  that we aim to achieve is \(\omega = p_3 + \sum _{i = 1}^{m} \omega _i\) .
